摘要
针对全波形反演问题的不适定性,本文将基于块的稀疏字典学习、图的拉普拉斯矩阵应用于全波形反演(Full Waveform Inversion,FWI)问题,提出了一种新的FWI算法—基于字典学习和图拉普拉斯正则化的全波形反演方法.利用奇异值分解从图像块中学习出具有自适应性的稀疏变换字典,在稀疏表示降噪模型的基础上,引入图拉普拉斯正则化项,同时考虑局部图像块的稀疏性和非局部图像块间的相似性.数值试验结果表明,与基于曲波变换的稀疏约束正则化波形反演算法相比,本文算法能够提供视觉上更清晰的反演结果,能够保留介质参数中更多的细节特征,且在峰值信噪比、结构相似性和均方根误差等定量指标上,都有明显地改善.
Full Waveform Inversion(FWI)is a highly nonlinear and ill-posed inverse problem,which needs proper regularization to produce reliable results.In this study,we propose a new FWI method based on dictionary learning and graph Laplacian regularization,which includes patch-based sparse dictionary learning and graph Laplacian.The proposed method first utilizes the Singular Value Decomposition(SVD)to learn the adaptive optimal sparse transform dictionary from image patches.Then,the graph Laplacian regularization term is introduced based on the sparse representation denoising model.Here,the sparsity of local image patches and the similarity of non-local image patches are considered simultaneously.We carried out numerical simulations and compared with the sparse constraint regularization FWI method based on curvelet transform.Experimental results show that the new method retains more detailed features in media parameters,and has better visual effect.Meanwhile,it has significantly improved in Peak Signal-to-Noise Ratio(PSNR),Structural Similarity(SSIM)and Root Mean Square Error(RMSE).
作者
华然
傅红笋
杨露
HUA Ran;FU HongSun;YANG Lu(School of Science,Dalian Maritime University,Liaoning,Dalian 116026,China)
出处
《地球物理学进展》
CSCD
北大核心
2022年第3期1034-1040,共7页
Progress in Geophysics
基金
国家自然科学基金项目(41474102)资助。
关键词
全波形反演
字典学习
图拉普拉斯正则化
稀疏表示
Full Waveform Inversion(FWI)
Dictionary learning
Graph Laplacian regularization
Sparse representation
